How to plot a function $f(x)=\frac{3(4+x)}{3(2-x)-16}$ (say $x \in [-15,15]$ ) with the condition that i want to give different color for each of the following cases
(i) when $\frac{x+4}{3x+10}>0$ and $\frac{x^2+8x+12}{3x+10}>0$
(ii) when $\frac{x+4}{3x+10}>0$ and $\frac{x^2+8x+12}{3x+10}<0$
(iii) when $\frac{x+4}{3x+10}<0$ and $\frac{x^2+8x+12}{3x+10}>0$